On string loops in Calabi-Yau orientifolds in large volume

TL;DR

This paper develops a method to compute string-loop amplitudes in Calabi-Yau orientifold compactifications using string field theory, focusing on D1-instanton partition functions and divergence cancellations in the large volume limit.

Contribution

It introduces a patch-by-patch approach to compute string-loop amplitudes in Calabi-Yau orientifolds, addressing divergence issues and setting the stage for further results on superpotential normalization and moduli renormalization.

Findings

Computed the one-loop partition function of D1-instantons in a specific orientifold setting.

Demonstrated cancellation of unphysical divergences via vertical integration.

Laid groundwork for future analysis of superpotential normalization and Kähler moduli renormalization.

Abstract

We explain and illustrate how to compute string-loop amplitudes in Calabi-Yau orientifold compactification in the large volume limit with the help of the patch-by-patch description of string field theory. We compute the one-loop partition function of the D1-instanton in type IIB string theory compactified on an O9 orientifold of a Calabi-Yau threefold to the first order in the large volume expansion. We show that the unphysical divergence arising from a naive choice of PCOs is canceled by vertical integration. The corollaries of this result, including the universal part of the normalization of the D-instanton superpotential and the one-loop renormalization of K\"ahler moduli, will be presented elsewhere.